Question 334642
<font face="Garamond" size="+2">


A solution of an equation is any entity that can be substituted for the variable or variables such that the the equation is a true statement.


For example, consider the equation *[tex \Large x\ +\ 3\ =\ 8]


It should be clear that if you replace the *[tex \Large x] with *[tex \Large 5], then you have a true statement because 5 plus 3 does indeed equal 8.  But if you replace *[tex \Large x] with any other number, then you have a false statement.  Let's see what happens if we use *[tex \Large 2].  2 plus 3 is 5 which is most assuredly not equal to 8.  And the same thing would happen for any other number besides 5 substituted for *[tex \Large x].


Point of semantics:  You said "...number to be <b>the</b> "solution"..."


Using the word <b>the</b> in that context is only appropriate when you have single variable linear equations.  It is more appropriate to say "...a solution" because, in general, there may be more than one.  For example, *[tex \Large x^2\ +\ 2x\ -\ 3\ =\ 0] has two solutions, namely *[tex \Large 1] and *[tex \Large -3] (try it and see for yourself).


Furthermore, some equations have solutions that are not numbers, but ordered pairs of numbers.  You see this when you have two-variable equations.  For instance, *[tex \Large 2x\ -\ y\ =\ 3], has an infinite number of solutions one of which is *[tex \Large (2,1)].


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
</font>